In a practical fading environment, the transmission rate to each user in the coverage area depends on the random channel capacity (i.e., instantaneous achievable rate), which is a function of the amount of resources, e.g., bandwidth, supplied to the downlink [1]}, [2]}, [3]}. In the proposed model, we do not make any assumption about the type of allocated transmission resources in APs. This can be power, bandwidth, or time-slot. Since a path connects a data center to a user, a given path uniquely identifies the downlink by which a user is served. The achievable rate of a downlink, denoted by \(v_k^p\) , can follow any arbitrary PDF. Let \(z_{k,L_n}^p(v_k^p,t_k^p)\)  denote the PDF of the achievable rate of the downlink of path \(p\)  in the \(n^\text{th}\)  long time-scale, where the amount of the transmission resource supplied to the downlink is \(t_k^p\) . The CDF of the downlink achievable rate is denoted by \(Z_{k,L_n}^p(v_k^p,t_k^p)\)  in the \(n^{\text{th}}\)  long time-scale and determines the probability that the achievable rate of the downlink of path \(p\)  to serve user \(k\)  is at most \(v_k^p\) . When the random achievable rate of a downlink is less than the reserved rate \(r_k^p\) , the experienced outage is \(r_k^p-v_k^p\) . The probability that this amount of outage occurs in the \(n^{\text{th}}\)  short time-scale is \(z_{k,S_n}^p(v_k^p,t_k^p)\) . In light of the above arguments, the expected value of the outage of the downlink of path \(p\)  is obtained as
\(\int _{0}^{r_k^p}z_{k,S_n}^p(v_k^p,t_k^p)\:(r_k^p-v_k^p)dv_k^p,\hspace{14.22636pt}\forall p\in \mathcal {P}_k,\forall k.\) 
